Magnetotransport properties of two-dimensional GaN and GaAs electron systems

此篇論文主要描述在低溫和外加磁場下，二維氮化鎵電子系統及含有砷化銦量子點的砷化鎵電子系統之傳輸性質，本論文包含下列兩個主題： 1. 低磁場下氮化鋁鎵/氮化鎵二維電子系統電性量測之研究 我們研究了高載子濃度的氮化鋁鎵/氮化鎵二維電子系統在外加垂直磁場下電子的傳導特性，在外加低磁場時，不同溫度下所量測到的縱向電阻率均與磁場的平方項成正比，這個結果可以利用在低亂度電子系統中的庫侖交互作用力來解釋，在高磁場時，縱向電阻率在臨界磁場處產生了一個不隨溫度變化的交點，我們發現在此臨界磁場處縱向電阻率等於霍耳電阻率。經由分析縱向電阻振盪的部分，我們得到電子的量子遷移率小於古典遷移率，這在古典理論中是不合理的，然而在此實驗結果中，我們觀察到在磁場高於臨界值時，縱向電阻率隨著溫度上升而增加，此現象與量子霍耳態相同，因此我們推論這兩者的不同是由於高磁場的定域效應所引起。 2. 在低磁場下從絕緣態到量子霍耳液體態電子導電行為之研究 我們利用了具有閘極且含有自身聚集形成的砷化銦量子點的二維砷化鎵電子系統來研究在低溫、低磁場下電子的導電行為。在此研究中，我們發現在低場的絕緣態與高場的量子霍耳態之間，縱向電阻率有多個不隨溫度變化的交點，而此交點所在的位置與其所伴隨振盪的振幅可以利用Shubnikov-de Haas 理論解釋，因此由我們的實驗結果可以看出，在低場絕緣態與高場量子霍耳液體態之間，的確存在一個過渡的金屬態。The thesis describes the low-temperature magnetotransport properties of a GaN two-dimensional electron gas and a GaAs two-dimensional electron gas containing self-assembled InAs quantum dots. This thesis comprises the following two parts: 1. Low-field magnetoresistivity measurements on an AlGaN / GaN 2D electron system We have studied the transport properties of a high-carrier-density AlGaN/GaN two-dimensional electron system in the presence of a perpendicular magnetic field B. At low magnetic fields, the measured longitudinal resistivity shows a parabolic B-dependence at various temperatures. This effect can be ascribed to electron-electron interaction effects in a weakly disordered electron system. At high magnetic field, there is a temperature-independent point in at the critical magnetic field Bc. We find that, at this crossing point, the Hall resistivity is approximately equal to longitudinal resistivity. By analyzing the amplitude of the observed Shubnikov-de Haas oscillations at high magnetic field, we find that the quantum mobility is smaller than classical mobility. It could be due to high-field localization effect which gives rise to the formation of a quantum Hall liquid-like state since longitinal resistivity increases with increasing temperature for B > Bc. 2. From insulator to quantum Hall liquid at low magnetic fields We have performed low-temperature transport measurements on a GaAs two-dimensional electron system containing self-assembled InAs quantum dots at low magnetic fields. In our study, multiple temperature-independent points and accompanying oscillations are observed in the longitudinal resistivity between the low-field insulator and the quantum Hall liquid. The amplitudes of these oscillations can be well described by conventional Shubnikov-de Haas theory, and our experimental results therefore support the existence of an intermediate metallic regime between the low-field insulator and quantum Hall liquid.Contents Chapter 1 Introduction to two-dimensional electron systems 1 1.1 Introduction...........................................................................................................1 1.1.1 Mesoscopic physics.....................................................................................1 1.1.2 Two-dimensional electron system................................................................2 1.2 The modulation doped GaAs/AlGaAs heterostructure.........................................3 1.3 Varying carrier concentration in a 2DES..............................................................4 1.4 References.............................................................................................................5 Chapter 2 Theoretical Background: Electron transport in a two-dimension electron system 6 2.1 The Drude theory..................................................................................................6 2.1.1 Basic assumptions........................................................................................7 2.1.2 Hall effect and classical magnetoresistance.................................................9 2.2 Quantum mechanics and a 2D electron gas........................................................10 2.2.1 Density of states.........................................................................................11 2.2.2 Landau quantization...................................................................................12 2.2.3 Shubnikov-de Haas effect..........................................................................14 2.2.4 Integer quantum Hall effect.......................................................................14 2.3 References...........................................................................................................17 Chapter 3 Experimental techniques and equipments 18 3.1 HelioxTL system..................................................................................................18 3.2 HelioxTL inserts...................................................................................................19 3.3 Principle of operation..........................................................................................20 3.3.1 Low temperature operation........................................................................20 3.3.2 High temperature operation.......................................................................21 3.4 Four-terminal resistance measurements..............................................................21 3.5 References...........................................................................................................23 Chapter 4 Low-field magnetoresistivity measurements on an AlGaN/GaN 2D electron system 24 4.1 Introduction.........................................................................................................25 4.2 Previous work.....................................................................................................26 4.2.1 Quantum corrections to conductivity.........................................................26 4.2.2 Quantum phase transition at low B-fields..................................................28 4.3 Experiment..........................................................................................................29 4.4 Results and discussion........................................................................................31 4.5 Conclusion..........................................................................................................37 4.6 References...........................................................................................................38 Chapter 5 From insulator to quantum Hall liquid at low magnetic fields 40 5.1 Introduction.........................................................................................................41 5.2 Previous work.....................................................................................................43 5.2.1 Unifying model for several classes of 2D phase transition.......................43 5.2.2 Intermediate metallic regime.....................................................................44 5.3 Experiment..........................................................................................................45 5.4 Results and discussion........................................................................................46 5.5 Conclusion..........................................................................................................51 5.6 References...........................................................................................................52 Chapter 6 Conclusions 5